Motion along the axis of a discrete channel variableα

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Abstract
In the system of coupled Schrödinger equations one can define a kinetic energy operator, corresponding to ‘‘interchannel wave propagation.’’ Exactly solvable models of motion along the axis of a discrete variable α, which numbers the channels (analogs of the rectangular well, Bargmann-type potentials, etc.), can be constructed. Thus the intuition developed in considering wave propagation in ordinary configuration space is easily transferred to the new dimension α. Particularly, there may exist resonances or bound states of a special nature corresponding to the α standing waves. The same idea of α motion allows one to consider the old problem of wave propagation in periodic potentials from a new viewpoint.

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